document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163060>Question 1163060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
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document.write( "A clothing shop paid $1,620 for suits to be sold at a profit of $15 each. When he had sold all but 9 suits, he had recovered the cost. Assuming that each suit cost the same,how many did he buy and how much did he pay for each one.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787014 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=787014\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let c be the cost of each suit.<BR>\n" );
document.write( "let s be the selling price of each suit.<BR>\n" );
document.write( "then xc = total cost and xs = total selling price.<BR>\n" );
document.write( "you are given that 1620 is the total cost.<BR>\n" );
document.write( "this means that xc = 1620<BR>\n" );
document.write( "you are given that the total cost is achieved when all but 9 suits are sold.<BR>\n" );
document.write( "this means that xc = (x - 9) * s.<BR>\n" );
document.write( "since xc = 1620, you get:<BR>\n" );
document.write( "1620 = (x - 9) * s<BR>\n" );
document.write( "you are given that the profit on each suit is 15.<BR>\n" );
document.write( "this means s = c + 15<BR>\n" );
document.write( "therefore:<BR>\n" );
document.write( "1620 = (x - 9) * (c + 15)<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "1620 = xc + 15x - 9c - 15*9<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "1620 = xc + 15x - 9c - 135<BR>\n" );
document.write( "since xc = 1620, this becomes:<BR>\n" );
document.write( "1620 = 1620 + 15x - 9c - 135<BR>\n" );
document.write( "subtract 1620 from both sides of this equation to get:<BR>\n" );
document.write( "0 = 15x - 9c - 135<BR>\n" );
document.write( "add 35 to both sides of this euation to get:<BR>\n" );
document.write( "135 = 15x - 9c<BR>\n" );
document.write( "since xc = 1620, then c must be equal to 1620 / x<BR>\n" );
document.write( "replace c with 1620/x to get:<BR>\n" );
document.write( "135 = 15x - 9*1620/x<BR>\n" );
document.write( "multiply both sides of this equation by x to get:<BR>\n" );
document.write( "135x = 15x^2 - 14580<BR>\n" );
document.write( "subtract 135x from both sides of the equation to get:<BR>\n" );
document.write( "0 = 15x^2 - 135x - 14580<BR>\n" );
document.write( "divide both sides of this equation by 15 to get:<BR>\n" );
document.write( "0 = x^2 - 9x - 972<BR>\n" );
document.write( "factor this equation to get:<BR>\n" );
document.write( "(x + 27) * (x - 36) = 0<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 36 or x = -27<BR>\n" );
document.write( "x has to be positive, so x = 36.<BR>\n" );
document.write( "go back to your original equations to get:<BR>\n" );
document.write( "xc = 36*x = 1620<BR>\n" );
document.write( "solve for c to get c = 45.<BR>\n" );
document.write( "since s = c + 15, then s = 60.<BR>\n" );
document.write( "your total cost is when all but 9 suits are sold.<BR>\n" );
document.write( "this means that (x-9) * 60 = 1620<BR>\n" );
document.write( "since x = 36, this becomes 27 * 60 = 1620 which becomes 1620 = 1620.<BR>\n" );
document.write( "this confirms that x = 36 is correct.<BR>\n" );
document.write( "the cost for each suit is 1620/36 = 45.<BR>\n" );
document.write( "that's your solution.<BR>\n" );
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